This paper describes a novel approach to the compression of fingerprint images using new mathematical transform, namely, the curvelet transform that has proven to show promising results over ridgelet and wavelet transforms. Wavelets are well suited to point singularities, however they have a problem with orientation selectivity, and therefore, they do not represent two-dimensional singularities (e.g. smooth curves) effectively. Ridgelets provide sparse representation to smooth objects with straight edges. But in image processing, edges are typically curved rather than straight. However at sufficiently fine scales, a curved edge is almost straight. By deploying ridgelets in a localized manner, a new transform considered in this paper has been developed and it can capture the curved edges effectively. A comparision has been carried out among Wavelets, Ridgelets and Curvelets based compression techniques for fingerprint image. A high quality compression has been achieved using curvelets compared to the existing Techniques.